The ability to drastically slow down the propagation speed of light, and to coherently stop and store optical pulses, holds the key to the ultimate control of light, and has profound implications for optical communications and quantum information processing. See R. Ramaswami, K. N. Sivarajan, Optical Networks: A Practical Perspective (Morgan Kaufmann, San Francisco, Calif., 1998)] and M. D. Lukin, A. Imamoglu, Nature 413,273 (2001); and L. M. Duan, M. D. Lukin, J. I. Cirac, P. Zoller, Nature 414,413 (2001). In order to reduce the group velocity of light coherently, there are two major approaches, which employ either electronic or optical resonances. Using electronic resonances in atomic systems, the group velocity of light can be decreased by several orders of magnitude. See L. Brillouin, Wave Propagation and Group Velocity (Academic, New York, 1960). Furthermore, with the use of quantum interference schemes such as the Electromagnetically Induced Transparency (EIT), the absorption at some electronic resonances can be strongly suppressed. See K. J. Boiler, A. Imamoglu, S. E. Harris, Phys. Rev. Lett. 66,2593 (1991). Dramatic slow down or even complete stop of light pulses can then be accomplished by converting the optical signal into coherent electronic states. See A. Kasapi, M. Jain, G. Y. Yin, S. E. Harris, Phys. Rev. Lett. 74,2447 (1995); L. V. Hau, S. E. Harris, Z. Dutton, C. H. Behroozi, Nature 397, 594 (1999); M. M. Kash et. al, Phys. Rev. Lett. 82, 5229 (1999); D. Budker, D. F. Kimball, S. M. Rochester, V. V. Yashchuk, Phys. Rev. Lett. 83, 1767 (1999); C. Liu, Z. Dutton, C. H. Behroozi, L. V. Hau, Nature 409, 490 (2001); D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, M. D. Lukin, Phys. Rev. Lett. 86, 783 (2001); A. V. Turukhin et. al, Phys. Rev. Lett. 88, 236021 (2002); M. S. Bigelow, N. N. Lepeshkin, R. W. Boyd, Phys. Rev. Lett. 90,113903 (2003).
The use of electronic states to coherently store the optical information, however, imposes severe constraints on the operating conditions. As a result, only a few very special and delicate electronic resonances available in nature possess all the required properties. All the demonstrated operating bandwidths are far too small to be useful for most purposes. The wavelength ranges where such effects can be observed are also very limited. Furthermore, while promising steps have been taken for room temperature operation in solid-state systems, it still remains a great challenge to implement such schemes on-chip with integrated optoelectronic technologies. See A. V. Turukhin et. al, Phys. Rev. Lett. 88, 236021 (2002); and M. S. Bigelow, N. N. Lepeshkin, R. W. Boyd, Phys. Rev. Lett. 90,113903 (2003).
Consequently, it is of great interest to pursue the control of light speed using optical resonances in photonic structures including dielectric micro-cavities and photonic crystals. See Y. Yamamoto, R. E. Slusher, Phys. Today 46,66 (1993); E. Yablonovitch, Phys. Rev. Lett. 58,2059-2062 (1987); S. John, Phys. Rev. Lett. 58,2486-2489 (1987); and J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton, N.J., 1995).
Photonic structures can be defined by lithography and designed to operate at any wavelength range of interest. Ultra-high quality-factor cavities have been realized on semiconductor chips, and group velocities as low as 10−2 c for pulse propagation with negligible distortion have been experimentally observed in photonic crystal waveguide band edges or with Coupled Resonator Optical Waveguides (CROW). See D. K. Armani, T. J. Kippenberg, S. M. Spillane, K. J. Vahala, Nature 421, 925 (2003); M. Notomi et. al, Phys. Rev. Lett. 87,253902 (2001); See N. Stefanou, A. Modinos, Phys. Rev. B 57,12127 (1998); A. Yariv, Y. Xu, R. K. Lee, A. Scherer, Opt. Lett. 24, 711-713 (1999); and M. Bayindir, B. Temelkuran, E. Ozbay, Phys. Rev. Lett. 84,2140-2143 (2000). Nevertheless, such structures are fundamentally limited by the so-called delay-bandwidth product. See, for example, G. Lenz, B. J. Eggleton, C. K. Madsen, R. E. Slusher, IEEE Journal of Quantum Electronics 37, 525 (2001). The group delay from an optical resonance is inversely proportional to the bandwidth within which the delay occurs. Therefore, for a given optical pulse with a certain temporal duration and corresponding frequency bandwidth, the minimum group velocity achievable is limited. In a CROW waveguide structure, for example, the minimum group velocity that can be accomplished for pulses at 10 Gbit/s rate with a wavelength of 1.55 μm is no smaller than 10−2 c. For this reason, up to now, photonic structures could not be used to stop light.
The capability to reverse a wave in time has profound scientific and technological implications. In the field of acoustics or electronics, where the frequencies of the waves are low, time reversal of pulses can be accomplished through electronic sampling, recording, and playing back. For acoustic waves in particular, such processes has led to the developments of a wide variety of novel applications such as detection through random media, adaptive optics and sub-wavelength focusing. See M. Fink, “Time reversal of Ultrasonic Fields-Part I: Basic Principles”, IEEE Trans. Ultrason., Ferroelec, Freq. Contr., 39, 555 (1992); F. Wu, J. Thomas, M. Fink, “Time reversal of Ultrasonic fields-Part II: Experimental Results”, IEEE Trans. Ultrason., Ferroelec, Freq. Contr., 39, 567 (1992); I. Freund, “Time-reversal symmetry and image reconstruction through multiple-scattering media”, J. Opt. Soc. Am. A, 9, 456,1992; and J. de Rosny, M. Fink, “Overcoming the Diffraction Limit in Wave Physics Using a Time-Reversal Mirror and a Novel Acoustic Sink”, Phys. Rev. Lett. 89,124301 (2002).
The time reversal of an optical pulse is quite important in signal processing, and dispersion compensation in communication systems. Till now all the schemes for time reversal operation required use of special materials and nonlinear processes, which technologically are quite restrictive. A two-dimensional or three-dimensional array of many such structures can have many applications (as special mirrors in free-space communications) or in warfare applications where electromagnetic pulses are used. Other applications include the possibility of making an extremely precise auto-correlator or other signal processing parts.
In the field of optics, it has also been recognized that time-reversal operation can be used to enable complete compensation of both linear and nonlinear pulse dispersions. See D. M. Marom, “Real-Time Spatial-Temporal Signal Processing with Optical nonlinearities”, IEEE Journal of Quantum Elec, 7, 683 (2001). Since the phase front of optical wave oscillates at a frequency that is far higher than electronic sampling rates, the only mechanisms available for time reversal requires the use of nonlinear optical processes such as near-degenerate four-wave mixing. See D. M. Pepper, “Nonlinear optical phase conjugation”, in Laser. Handbook, vol. 4. Amsterdam: North-Holland Physics, 1988, pp. 333-485. While degenerate four-wave mixing provides a mechanism for phase-conjugating a monochromatic wave, in order to perform an ideal time-reversal operations for an optical pulse perfect phase-matching in principle need to be satisfied over the entire pulse bandwidth, which presents a challenge to the developments of suitable nonlinear optical materials. In addition, such a process typically requires the use a strong pump laser, which limits the possibility of on-chip integration.
It is therefore desirable to provide improved systems whereby the above described difficulties are alleviated.